Three Dimensional Geometry Question 207
Question: If the angle between the lines whose direction ratios are 2,?1 , 2 and a, 3, 5 be $ 45{}^\circ $ , then a =
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: D
Solution:
$ \cos \theta =\frac{a_1a_2+b_1b_2+c_1c_2}{\sqrt{a_1^{2}+b_1^{2}+c_1^{2}}\sqrt{a_2^{2}+b_2^{2}+c_2^{2}}} $ $ \frac{1}{\sqrt{2}}=\frac{2a-3+10}{\sqrt{1^{2}+2^{2}+1^{2}},\sqrt{a^{2}+3^{2}+5^{2}}} $
$ \Rightarrow 9,(a^{2}+34)=2,{{[2a+7]}^{2}}=,2,[4a^{2}+28a+49] $
$ \Rightarrow a^{2}-56a+208=0\Rightarrow a=4 $ .
BETA
